Stability analysis for neural networks with discrete and leakage
time-varying delay systems with delay-range-dependence and
delay-derivative-dependence
Abstract
The paper deals with the stability problem of neural networks with
discrete and leakage interval time-varying delays. Firstly, a novel
Lyapunov-Krasovskii functional was constructed based on the neural
networks leakage time-varying delay systems model. The delayed
decomposition approach (DDA) and integral inequality techniques (IIA)
were altogether employed, which can help to estimate the derivative of
Lyapunov-Krasovskii functional and effectively extend the application
area of the results. Secondly, by taking the lower and upper bounds of
time-delays and their derivatives, a criterion on asymptotical was
presented in terms of linear matrix inequality (LMI), which can be
easily checked by resorting to LMI in Matlab Toolbox. Thirdly, the
resulting criteria can be applied for the case when the delay derivative
is lower and upper bounded, when the lower bound is unknown, and when no
restrictions are cast upon the derivative characteristics. Finally,
through numerical examples, the criteria will be compared with relative
ones. The smaller delay upper bound was obtained by the criteria, which
demonstrates that our stability criterion can reduce the conservatism
more efficiently than those earlier ones.